ATI Radeon HD 7770 no GPU rendering?
OpenCL isn't fully supported yet (which is what AMD/ATI cards use to render):


  Cycles has two GPU rendering modes: through CUDA, which is the
  preferred method for NVidia graphics cards; and OpenCL, which is
  intended to support rendering on AMD/ATI graphics cards. The
  implementation of OpenCL is only in an experimental stage and disabled
  in official builds. (source)


You could try to find a build on GraphicAll, but there is no guarantee it'll work.

I would recommend just rendering it on CPU. If you are really pressed for time, there are a few things you can do to speed things up:


Set the size of the tiles lower (Render Tab > Performance). The CPU renders faster if the tiles are smaller (GPU renders faster on bigger tiles).
Set the threads to fixed and set them as high as possible (Render Tab > Performance). This will make Blender use more threads which will speed up the render.
Turn the samples down. It's fairly easy to remove a few fireflies later on in compositing, and will speed up your render time a lot.